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The primal-dual second-order cone approximations algorithm for symmetric cone programming.

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The primal-dual second-order cone approximations algorithm for symmetric cone programming.

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Title: The primal-dual second-order cone approximations algorithm for symmetric cone programming.
Author: Chua, Chek Beng.
Copyright year: 2007
Abstract: Given any open convex cone K, a logarithmically homogeneous, self-concordant barrier for K and any positive real number r < 1, we associate, with each direction x 2 K, a second-order cone ˆKr(x) containing K. We show that K is the interior of the intersection of the second-order cones ˆKr(x), as x ranges over all directions in K. Using these second-order cones as approximations to cones of symmetric, positive definite matrices, we develop a new polynomial-time primal-dual interior-point algorithm for semidefinite programming. The algorithm is extended to symmetric cone programming via the relation between symmetric cones and Euclidean Jordan algebras.
Subject: DRNTU::Science::Mathematics::Applied mathematics::Optimization.
Type: Journal Article
Series/ Journal Title: Foundations of Computational Mathematics.
School: School of Physical and Mathematical Sciences
Rights: Foundations of computational mathematics @ copyright 2000 Springer Verlag. The jourmal's websites is located at http://www.springerlink.com.ezlibproxy1.ntu.edu.sg/content/106038/
Version: Accepted version

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